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Area of Science:

  • Fluid dynamics
  • Geophysics
  • Mechanical engineering

Background:

  • Analyzing fluid flow coherence is crucial for understanding complex systems.
  • Traditional methods often require dense trajectory data or assumptions about velocity fields.
  • Objective, observer-independent measures are needed for robust analysis.

Purpose of the Study:

  • To derive novel, quasi-objective measures of local material stretching and rotation.
  • To enable computation from individual trajectories, reducing data requirements.
  • To identify and visualize Lagrangian Coherent Structures (LCS) in fluid flows.

Main Methods:

  • Developed local material stretching and rotation estimators.
  • Defined a condition for quasi-objectivity based on trajectory accelerations and vorticity.
  • Applied measures to sparse trajectory data for structure identification.

Main Results:

  • Measures are computable from individual trajectories, independent of others.
  • Quasi-objective measures approximate objective coherence diagnostics under specific conditions.
  • Demonstrated effectiveness in highlighting elliptic and hyperbolic LCS with sparse data.

Conclusions:

  • The new quasi-objective measures offer a practical approach to analyzing fluid flow coherence.
  • These methods enhance the identification of key flow structures from limited observational data.
  • Applicable across various scientific domains relying on trajectory analysis.